# Boat and Stream

Assume given Speed in still water = a km/h,

Rate of the stream = b km/h

Then, Rate in downstream = a+b km/h

Rate in upstream = a-b km/h

Assume given Downstream = x km/h

Upstream = y km/h

Then Speed in still water = (x + y) / 2

Rate of the stream =(x - y) / 2

Problems

Q1

The speed of a boat in still water is 15 km/h and the rate of the stream is 3 km/h. Find the speed in downstream and upstream.

Speed in still water = 15 km/h

Rate of the stream = 3 km/h

Speed in downstream = 15 + 3 = 18 km/h

Speed in upstream = 15 – 3 = 12 km/h

Q2

A man can a row a boat 12km/h with the stream and 8km/h against the stream. Find the speed in still water?

Downstream = 12 km/h

Upstream = 8 km/h

Speed in still water = (12 + 8) /2 = 10 km/h

Q3

A man can row a boat 15 km/h with the current and speed of the current is 3 km/h. Find his speed against the current?

Downstream = 15 km/h

Rate of the stream = 3 km/h

Rate of the stream = (Downstream - Upstream) / 2

3 = (15 - upstream) / 2

Upstream = 15 – (3 X 2) = 15 – 6 = 9km/h

Q4

A man can row a boat 40km downstream in 5hrs and 18 km upstream in 3hrs.Find the speed of the current?

Downstream = 40 / 5 = 8km/h

Upstream = 18 / 3 = 6km/h

Rate of the stream = (8 - 6) / 2 = 2/2 = 1km/h

Q5

A man can row a boat to a certain distance upstream in 4 hrs and takes 3hrs to row downstream the same distance. What is the speed of the boat in still water if the speed of the stream is 2km/h.

Speed in still water = speed of the stream X (t1+t2) / (t1-t2)

= 2 (4 + 3) / ( 4-3) = 14 km/h

Q6

A man can row a boat to a certain distance upstream in 6hrs and takes 4hrs to row downstream the same distance. What is the speed of the stream if the speed of the boat in still water is 20km/h.

Rate of the stream = speed of the boat in still water X (t1-t2) / (t1+t2)

= 20 (6-4) / (6+4) = 4 km/h